2022 VJC Promo Q4

The curve \({{C}_{1}}\) has equation \(y={{x}^{3}}+1\) and the curve \({{C}_{2}}\) has equation \(y=b{{\left( -x+a \right)}^{3}}+b\), where \(a\) and \(b\) are positive constants.

1. Describe a sequence of transformations that transforms \({{C}_{1}}\) onto \({{C}_{2}}\).[3]
2. The stationary point on \({{C}_{1}}\) corresponds to the point \(\left( k,l \right)\) on \({{C}_{2}}\) after the sequence of transformations in part (i). Find \(k\) and \(l\) in terms of \(a\) and \(b\).[2]